A copula-based interval-bistochastic programming method for regional water allocation under uncertainty

Abstract

In regional water resources allcoation problems, the uncertainties of hydrological variables and socio-economic parameters are bringing huge challenges to water managers. So far, the stochastic programming models have difficulty in addressing uncertain problems, in which there are two correlated random variables. In order to address regional water resources allocation under two hydrological random variables and interval parameters, a couple-based interval-bistochastic programming (CIBSP) method is proposed. The CIBSP method includes several key steps: first, the marginal distributions of the two hydrological variables are analyzed and hydrological scenarios are set; then, the copula is chosen to analyze joint probability distribution of the two hydrological variables and the joint probabilities of scenarios are calculated; last, an interval-bistochastic model is formulated by incorporating two-stage stochastic programming, interval-parameter programming, and bivariate joint distribution. The CIBSP method can describe the probability of occurrence of a hydrological scenario and then make an optimized water allocation scheme under uncertainties. To demonstrate its applicability, the CIBSP method is applied to the Zhanghe Irrigation District located in China, to optimize available water allocation under the uncertainties of the annual inflow volume of the Zhanghe Reservoir and annual rainfall volume in the irrigated district. An appropriate water allocation plan can be obtained by the method, which provides a foundation to water managers for managing water resources in Zhanghe Irrigation District. Moreover, other two hypothetical situations named independence hypothetical situation and linear relationship hypothetical situation are discussed. The difference in the results between the two hypothetical situations and the case study indicates that an appropriate description of the joint probability of the annual inflow volume and annual rainfall volume by using CIBSP method is important for water resource allocation under uncertainties.